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Lets Have Fun With Algebra
First, let us try to define the word ALGEBRA.
What is Algebra?
Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary over time.
These variables include things like the relationship between supply of an object and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are referred to as variables.
This definition is taken from web, [http://cstl.syr.edu/fipse/Algebra/Unit1/algebra.html]
Let us look at what an expression is:
An expression is a meaningful collection of numbers, variables, and signs, positive or negative, of operations that must make mathematical and logical sense.
Some info. taken from website, http://www.cstl.syr.edu/fipse/Algebra/Unit1/algebra.html
- contain any number of algebraic terms
- use signs of operation—addition, subtraction, multiplication, and division.
- do not contain an equality sign (=)
Some examples of an expression are:
Please note that in these examples, the expressions consist of coefficients and variables.
In example (1) [7, 4, and -2] are called coefficients and [x, y and z] are the variables.
Example1 consists of three terms separated by the + and - signs; they are, (7x); (4y) and (-2z).
A term with no sign infront of it, is positive.
A variable, as the word suggests, varies and so the variables x,y and z can take on different values. That is why letters or symbols are used to represent them, because we do not know what they are.
Whats The Difference Between an EXPRESSION and an EQUATION?
Simply put, expressions are those 3 examples above, they do not have an (=) sign included.
An equation consists of an equal sign (=) as shown below.
8x-6y+2z = 12. In otherwords, an equation has a LEFT side and a RIGHT side.
You also need to remember that, if we place an equal sign (=) in the example above, then we are really saying that what you have on the LEFT is EQUAL to what is on the RIGHT.
x, y & z will have to take on numerical values, so that when the equation is solved, the answer will be 12 as seen in the equation above.
Let us say that x= 2, y=2 and z=4
now, if we want to solve the equation above which is:
8x-6y+2z = 12, since we know what the three variables are, we can substitute them into the equation as shown below.
8(2)- 6(2) +2(4) = 12
8*2 = 16
6*2 = 12, and
2*4 = 8, therefore
16 -12 + 8, must give you a value of 12 as in the equation above.
let us see if it works.
16 -12 + 8 =12, when simplified would be
16 - 12 = 4, and then you have to add 8 to 4 which is 4+8 which is equal to 12.
Hence the LEFT side of the equation is EQUAL to the RIGHT side of the equation.
I would like for you to try these examples below.
- If x= 2, y= 4 and z= 3, prove that the left side of the equation is equal to the right side.
- 9x - 2y - 2z = 4
- 12x + 3y + 4z = 4
In my next blog, I'll show you how to find the unknown variable in an algebraic equation.
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